Yu Yevon is notorious for being an easy final boss, so much that Braska's Final Aeon is often cited as the game's true final boss. Yu Yevon's main offensive attack, Gravija, an attack that even harms himself, removes 75% of the party members' total HP and cannot KO. He can also use Osmose and Ultima, but only when his HP is low.
All party members have permanent Auto-Life (supposedly bestowed by the fayth to help Yuna defeat Yu Yevon) so losing the battle is impossible, unless one does so deliberately by incapacitating the party with status effects, such as petrification. The real hindrance to beating Yu Yevon is that he automatically casts Curaga on himself, which restores 9,999 HP, every time he takes damage, and as in the previous battles, the Yu Pagodas will occasionally heal him.
One strategy is to ensure that characters are equipped with weapons with the Break Damage Limit ability. The other trick is easier: Yu Yevon is susceptible to the Zombie which can be inflicted with Zombie Attack. This way, restorative items and spells, including those of the Pagodas and Yu Yevon's own Curaga, will harm him, whereas resurrecting items and magic will kill him instantly. Reflect can also be cast on Yu Yevon to redirect his Curaga spells to the party, allowing the party to attack him with physical strikes until he dies.
Another strategy is to Doublecast magic for two 9,999s (or more with Break Damage Limit) every turn. Yu Yevon will only be able to use Curaga for one 9,999.
If the player doesn't wish to risk the chance of being hit with Ultima when Yu Yevon is weak, they may Use a Candle of Life on him to inflict Doom, and thus he will die instantly in three turns.
Another strategy requires no abilities whatsoever. The trick is to focus on keeping the Yu Pagodas incapacitated, while Yu Yevon slowly whittles down his own HP with his Gravija spells. Once the spells start doing 0 damage to him, it means he is down to 1 HP, and can be killed by any attack.
Limiting the healing potential of his Curaga spells is also an effective way of defeating him. Using Magic Break decreases the healing Curaga gives to around 5500. If coupled with the use of Shell on Yu Yevon, the healing potential drops to around 2700.
It is possible that Yu Yevon's boss fight was supposed to be a puzzle battle, where the party has to use the last strategy indicated. If so, the programmers made the mistake of not making him invulnerable to status ailments and effects, which would have forced the party to use that strategy (unless they have the Break Damage Limit ability).